Algebra Sleuth: Proof that 1 = 2?

Challenge your high school student to find the flaw in this short mathematical proof that one is equal to two.  This activity provides a good review of basic math principals and the structure of mathematical proofs. It’s also a good reminder that knowing math principals is good protection against getting tricked.

• The proof that 1 = 2 (below)

1. Show your teen the proof.
2. Ask her to tell you which step is invalid. She should determine both which number is wrong, and why.
3. Help her keep going until she understands the answer.

1) a = b                                                            1) Given

2) a2 = ab                                                         2) Multiply both sides by a

3) a2-b2 = ab-b2                                                3) Subtract b2 from both sides

4) (a+b)(a-b) = b(a-b)                                         4) Factor both sides

5) (a+b) = b                                                       5) Divide both sides by (a-b)

6) a+a = a                                                          6) Substitute a for b

7) 2a = a                                                            7) Addition